![]() ![]() On the other hand, there is another well-known feature about things that happen in the quantum world. This also explains why electrons are identical particles because all electrons are the excitation of a single quantized Dirac field. (Especially, the Quantum Electrodynamics, the QED, which is the quantum version of Electrodynamics.) In QED, photons are treated as the quantized electromagnetic waves, while electrons are treated as the quantized Dirac field of electron. In fact, to fully understand what photon is, we need a theory called Quantum Field Theory (QFT), which is the quantum version of classical field theory. However, problems involving photons are not usually addressed in the standard Quantum Mechanics. In other words, it’s a process that makes the order of performing position and momentum operators matter, thereby making the system “Quantum-Mechanicalized.”īy the way, you might guess that the existence of photon, which is the quantized electromagnetic waves, is also a result of Quantum Mechanics. Of course, here I’m talking about the original meaning of the word “Quantum.” Nowadays, people just use the word “quantization” as a technical term referring to “Quantum-Mechanicalization.” For instance, the jargon Canonical Quantization in Quantum Mechanics means that we take the commutator ≡ xp - px = iℏ, which was equal to zero in the classical case. It makes the sound waves which are the superposition of its base frequency and all harmonics that are frequencies equal to the integer multiples of the base frequency. For example, the vibration modes of a classical string with two fixed ends are quantized (e.g., the string in a violin). In classical physics, we also have a very similar situation. The momentum and the energy of a free particle are continuous.īeing quantized as a result of the boundary condition is not that mysterious and is not exclusive to Quantum Mechanics. ![]() For free particles in Quantum Mechanics, there is nothing really quantized. Also, the quantization of a component of Spin (e.g., the eigenvalue of S_z) is due to the periodic boundary condition of spacial rotation (i.e., exp or the world should look similar after a 360° rotation). For example, the allowed total energy of the electron in a Hydrogen atom is quantized is due to the fact that the electron is bounded by the Coulomb potential from the proton. The “quantized” property comes from the fact that you are asking the eigenvalue problem of a bounded system, or you can say it comes from the boundary condition. ![]() For example, the allowed energy level of the electron in the Hydrogen atom is quantized, i.e., we have 1s, 2s, 2p, …… all those discrete allowed orbitals with quantized or discrete allowed energies.Īlthough “Quantum” is one of the possible outcomes of Quantum Mechanics, quantization is not built inside the Quantum Mechanics. If you are learning Quantum Mechanics for the first time, or you are asked by a friend who wants to know about Quantum Mechanics, the first question you might have probably is why it is called “Quantum” Mechanics? A quick answer to this question is that Quantum Mechanics is a theory that can explain various quantized phenomena we encountered in experiments, which cannot be explained by Classical Mechanics. It’s like Newton’s Law: F=ma, which only works for the macroscopic objects, but is still valid in the microscopic world. Quantum Mechanics is a theory that describes how tiny stuff like electrons move around. Note: a Chinese version of this article is available here. ![]()
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